A robbery was reported as having been carried out by an African-American man with a beard and mustache in the company of a blond Caucasian woman with a ponytail who escaped in a yellow convertible. A couple fitting that description, the Collinses, was picked up. Faulty mathematics were use to infer “that there could be but one chance in 12 million that defendants were innocent and that another equally distinctive couple actually committed the robbery.” (See the Wikipedia page for how they arrived at this). A computation later in the Supreme Court of California Decision (People v. Collins, 68, Cal.2d 334, 335 (Cal. 1968)) figures that even with the prosecutor’s assumptions:

we would derive probability of over 40 percent that the couple observed by the witnesses could be “duplicated” by at least one other equally distinctive inter-racial couple in the area, including a Negro with a beard and mustache, driving a partly yellow car in the company of a blonde with a ponytail. Thus the prosecution’s computations, far from establishing beyond a reasonable doubt that the Collinses were the couple described by the prosecution’s witnesses, imply a very substantial likelihood that the area contained more than one such couple, and that a couple other than the Collinses was the one observed at the scene of the robbery.

We close with the closing words of the umbrella man:

If you have any fact, which you think is really sinister … is really obviously a fact that can only point to some sinister underpinnings … hey forget it, man, because you can never on your own think up all the non-sinister perfectly valid explanations for that fact. A cautionary tale.

We’re not stating an opinion on guilt or innocence in the above cases. We’re just encouraging a bit of reflection on what “beyond a reasonable doubt” should mean.